The logic of Refs. [1]}, [2]}, [3]} was as follows.
Consider the action of the form
\(S=\int d^{p+1}x{\rm Tr}\left(\frac{1}{2}F_{\mu \nu }^2+\frac{1}{2}(D_\mu X_I)^2+\frac{g^2}{4}[X_I,X_{J}]^2+{\rm fermion\ part}\right),\nonumber \) 
